The number of toy kangaroos, K, in a toy box after 't' days is given by K=t^2+20t. Estimate the rate at which the number of kangaroos is changing after 3 days?

$K = {t}^{2} + 20 t$

Apr 13, 2018

After 3 days, the number of kangaroos is increasing by 26 kangaroos per day.

Explanation:

The rate of change of a function is the derivative of that function.

First take the derivative of $K = {t}^{2} + 20 t$.
The derivative of ${t}^{n}$ is $n {t}^{n - 1}$ by the power rule.
So the derivative of ${t}^{2}$ is $2 t$.
The derivative of $a t$ is just $a$, so the derivative of $20 t$ is just $20$.
You should end up with $K ' = 2 t + 20$ when you add them together.

The question wants to know the rate of change after 3 days, so just plug in 3:
$K ' = 2 \left(3\right) + 20$
$K ' = 26$
So there you have it- after 3 days, the number of kangaroos is increasing by 26 kangaroos per day.